Wyniki wyszukiwania - BazTech

1

Stability of a Column Locally Resting on Winkler Elastic Foundation Under a Specific Load

Wasilewski M., Pisarski D., Bajer C. I.

Machine Dynamics Research

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2016

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Vol. 40, No. 1

65--82

EN

In this paper an online adaptive continuous-time control algorithm will be studied in the vibration control problem. The examined algorithm is a Reinforcement Learning based scheme able to adapt to the changing system’s dynamics and providing control converging to the optimal control. Firstly, a brief description of the algorithm is provided. Then, the algorithm is studied by the numeric simulation. The controlled model is a simple conjugate oscillator with sudden change of its rigidity. The effectiveness of the adaptation of the algorithm is compared to the simulation results of controlling the same object by the traditional Linear Quadratic Regulator. Because of the lack of constraints for a system size or its linearity, this algorithm is suitable for optimal stabilization of more complex vibrating structures.

2

On the semi-active control of carrying structures under a moving load

Pisarski D., Bajer C. I.

Vibrations in Physical Systems

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2010

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Vol. 24

325--330

EN

In this paper we address a group of recent research focused on the semi active control problems in carrying structures systems subjected to a travelling load. The magnitude of the moving force is assumed to be constant by neglecting inertial forces. The response of the system is solved in modal space. The optimal control problem is stated and it is solved by using of Pontryagin Maximum Principle. Switching control method is verified by numerical examples. The controlled system widely outperforms passive solutions. Due to its simplicity in practical design, the presented solution should be interesting to engineers.

PL

W pracy przedstawiono wyniki badań półaktywnego sterowania w układach nośnych poddanym obciążeniom ruchomym. Obciążenie zostało przedstawione jako bezinercyjne. Odpowiedź układu została wyznaczona w reprezentacji modalnej. Sformułowano zadanie sterowania optymalnego. Uzasadniono zastosowanie sterowań typu bang-bang opierając się na Twierdzeniu o Maksimum Pontryagina. Proponowana metoda sterowania została zweryfikowana na podstawie przykładów numerycznych. Wykazano przewagę układów sterowanych nad układami tłumienia pasywnego. Opracowana strategia sterowania jest prosta w implementacji i może być atrakcyjnym rozwiązaniem dla inżynierów.

3

Numerical methods for vibration analysis of Timoshenko beam subjected to inertial moving load

Dyniewicz B., Bajer C. I.

Vibrations in Physical Systems

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2010

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Vol. 24

87--92

EN

The paper deals with the problem of modeling of the moving mass particle in numerical computation by using the finite element method in one dimensional wave problems in which both the displacement and angle of the pure bending are described by linear shape functions. The analysis is based on the Timoshenko beam theory. We consider the simply supported beam, in a range of small deflections with zero initial conditions.

PL

Praca omawia problem modelowania numerycznego poruszającej się cząstki masowej metodą elementów skończonych w zadaniu jednowymiarowym. Przemieszczenia i obroty opisano liniowymi funkcjami kształtu. Analizę oparto na teorii belki Timoshenki.

4

New feature of the solution of a Timoshenko beam carrying the moving mass particle

Dyniewicz B., Bajer C. I.

Archives of Mechanics

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2010

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Vol. 62, nr 5

327-341

EN

The paper deals with the problem of vibrations of a Timoshenko beam loaded by a travelling mass particle. Such problems occur in a vehicle/track interaction or a power collector in railways. Increasing speed involves wave phenomena with significant increase of amplitudes. The travelling speed approaches critical values. The moving point mass attached to a structure in some cases can exceed the mass of the structure, i.e. a string or a beam, locally engaged in vibrations. In the literature, the travelling inertial load is often replaced by massless forces or oscillators. Classical solution of the motion equation may involve discussion concerning the contribution of the Dirac delta term, multiplied by the acceleration of the beam in a moving point in the differential equation. Although the solution scheme is classical and successfully applied to numerous problems, in the paper the Lagrange equation of the second kind applied to the problem allows us to obtain the final solution with new features, not reported in the literature. In the case of a string or the Timoshenko beam, the inertial particle trajectory exhibits discontinuity and this phenomenon can be demonstrated or proved mathematically in a particular case. In practice, large jumps of the travelling inertial load is observed.

5

Discontinuous Trajectory of the Mass Particle Moving on a String or a Beam

Dyniewicz B., Bajer C. I.

Machine Dynamics Problems

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2007

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Vol. 31, No. 2

66-79

EN

The paper deals with a new solution of the string or beam vibrating under a moving mass. Numerous solutions published up to date exhibit incorrect solutions. Moreover, they are not sufficiently simple and can not be applied to a whole range of the mass speed, also in over-critical range. We propose the solution of the problem that allows us to reduce the problem to the second order matrix differential equation. Its solution is characteristic of all features of the critical, sub-critical and over-critical motion. Results exhibit discontinuity of the mass trajectory at the end support point. The closed solution in the case of massless string is analysed and the discontinuity is mathematically proved. Numerical results obtained for inertial string demonstrate similar features. Small vibrations are analysed and that is why the effect discussed in the paper is of pure mathematical interest. However, the phenomenon can increase the complexity in discrete solutions.